I. Field of Invention
The present invention relates to both orthogonal frequency division multiple access OFDMA, to orthogonal Wavelet division multiple access OWDMA, to code division multiple access CDMA, and to multi-scale code division multiple access MS-CDMA, for cellular telephone and wireless data communications with data rates up to multiple T1 (1.544 Mbps), E1 (2.048 Mbps), Sonet, Ethernet, and higher (>10 Gbps), and to optical CDMA and optical OWDMA. Applications are to wire, wireless local area, wide area, mobile, point-to-point, and satellite communication networks. More specifically the present invention relates to a new and novel means for combining MS-CDMA with OFDMA, to a new and novel OWDMA which is an orthogonal multi-resolution complex Wavelet multiple access generalization of OFDMA, and to a new and novel means for combining MS-CDMA with OWDMA. This new architecture MS-CDMA OFDMA/OWDMA is an attractive candidate to replace current and future OFDMA applications and CDMA applications.
II. Description of Related Art
Current OFDMA art is represented by the applications to the wireless cellular communications standards IEEE 802.11a, IEEE 802.11g, IEEE 802.15.3a, IEEE 802.16. OFDMA uses the Fourier transform basis vectors as the orthogonal channelization vectors for communications with each basis vector multiplied by a symbol which is encoded with a data or pilot signal word.
The discrete Fourier transform DFT implemented as the fast Fourier transform FFT is defined in equations (1). Step 1 defines the digital sampling interval T over time, the sampling instants t=iT where i is the time index and where the sampling time 1/T is at least equal to the complex Nyquist sampling rate to prevent spectral foldover. Step 2 is the FFT of the complex baseband transmitted signal z(i) for the data block and step 3 defines the N×N orthogonal complex DFT matrix E row vectors E(k) which are the DFT harmonic vectors or basis vectors or code vectors or channelization vectors. Step 4 defines z(i) for one data block and is equal to the inverse FFT transform FFT−1 of the user symbols x(k).
                where 1/T≧ complex Nyquist sample rate        2 FFT of z(i)        
                              X          ⁡                      (            k            )                          =                  FFT          ⁡                      [                          z              ⁡                              (                i                )                                      ]                                                  =                              Σ            i                    ⁢                      E            ⁡                          (                              k                ,                i                            )                                ⁢                      z            ⁡                          (              i              )                                                              =                              Σ            i                    ⁢                      exp            ⁡                          (                                                -                  j                                ⁢                                                                  ⁢                2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                                  ki                  /                  N                                            )                                ⁢                      z            ⁡                          (              i              )                                                          3 DFT orthogonal harmonic code matrix E        
                    E        =                  NxN          ⁢                                          ⁢          DFT          ⁢                                          ⁢          orthogonal          ⁢                                                            ⁢                                                          ⁢          DFT          ⁢                                          ⁢          matrix                                        =                              [                          E              ⁡                              (                                  k                  ,                  i                                )                                      ]                    ⁢                                          ⁢          matrix          ⁢                                          ⁢          of          ⁢                                          ⁢          elements          ⁢                                          ⁢                      E            ⁡                          (                              k                ,                i                            )                                                                                    E            ⁡                          (                              k                ,                i                            )                                =                                    exp              ⁡                              (                                                      -                    j                                    ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                                      ki                    /                    N                                                  )                                      ⁢                                                  ⁢            harmonic            ⁢                                                  ⁢            k                          ,                  time          ⁢                                          ⁢          index          ⁢                                                            ⁢                                                          ⁢          i                                                  E          ⁡                      (            k            )                          =                  harmonic          ⁢                                                            ⁢                                                          ⁢          k          ⁢                                          ⁢                      basis            ⁢                                                                      ⁢                                                                    (            code            )                    ⁢                                          ⁢          vector                                        =                  [                                    E              ⁡                              (                                  k                  ,                  0                                )                                      ,                          E              ⁡                              (                                  k                  ,                  1                                )                                      ,            …            ⁢                                                  ,                          E              ⁡                              (                                  k                  ,                                      N                    -                    1                                                  )                                              ]                                                  EE          *                =        NI                                                      E            ⁡                          (              k              )                                ⁢                                    E              *                        ⁡                          (                              k                ′                            )                                      =                              δ            ⁡                          (                              k                -                                  k                  ′                                            )                                ⁢          NI                                                  where          ⁢                                          ⁢          I                =                  NxN          ⁢                                          ⁢          identify          ⁢                                          ⁢          matrix                                                  E          *                =                  complex          ⁢                                          ⁢          conjugate          ⁢                                          ⁢          transpose          ⁢                                          ⁢          of          ⁢                                          ⁢          E                                                  δ          ⁡                      (                          k              -                              k                ′                                      )                          =                  Dirac          ⁢                                          ⁢          delta          ⁢                                          ⁢          function                                        =                              1            ⁢                                                  ⁢            for            ⁢                                                  ⁢            k                    =                      k            ′                                                  =                  0          ⁢                                                            ⁢                                                          ⁢          otherwise                                    4 Transmitted DFT complex baseband signal z(i) for one data block        
                              d          ⁡                      (            k            )                          =                  data          ⁢                                          ⁢          modulation          ⁢                                          ⁢          for          ⁢                                                            ⁢                                                          ⁢          user          ⁢                                          ⁢          k                                        =                  encoded          ⁢                                          ⁢          amplitude          ⁢                                          ⁢                      A            ⁡                          (              k              )                                ⁢                                          ⁢          and          ⁢                                                            ⁢                                                          ⁢          phase          ⁢                                          ⁢                      φ            ⁡                          (              k              )                                                                        x          ⁡                      (            k            )                          =                  transmitted          ⁢                                                            ⁢                                                          ⁢          symbol          ⁢                                          ⁢          encoded          ⁢                                          ⁢          with          ⁢                                          ⁢                      d            ⁡                          (              k              )                                                              =                              A            ⁡                          (              k              )                                ⁢                                          ⁢                      exp            ⁡                          (                              j                ⁢                                                                  ⁢                φ                ⁢                                                                  ⁢                                  (                  k                  )                                            )                                                                        z          ⁡                      (            i            )                          =                              FFT                          -              1                                ⁡                      [                          x              ⁡                              (                k                )                                      ]                                                  =                              N                          -              1                                ⁢                      Σ            k                    ⁢                      x            ⁡                          (              k              )                                ⁢                                    E              *                        ⁡                          (                              k                ,                i                            )                                          
OFDMA for IEEE 802.11g in reference [1] is illustrated in FIG. 1. The channelization filter h(f) 1 covers a 20 MHz frequency band 2 assigned to OFDMA. Plotted is the power spectral density PSD=|h(f)|2 of this channelization filter h(f). A N=64 point fast Fourier transform FFT covers this band 2. Consistant with the IEEE specification, FIG. 1 refers to the DFT which is identical to the analog Fourier transform FT since it is the sampled data version of the FT. It is convenient to consider the DFT in this invention disclosure as the digital format for the FFT. The DFT frequency spectrum 3 consists of N=64 equally spaced filters 4 across this 20 MHz band. Filter spacing is equal to the DFT output rate 1/NT=0.3125 MHz=20 MHz/64. The DFT time pulse p(t) 5 is NT=3.2 μs in length and the total DFT period 6 is 4.0 μs which allows a 0.8 μs guard time for p(t).
Throughout this invention disclosure it will be understood that the FFT fast algorithm will always be used to implement the DFT and the inverse FFT−1 fast algorithm will always be used to implement the inverse DFT−1.
OFDMA transmitter encoding of the OFDMA waveform in FIG. 1 is defined in equations (2). Step 1 lists the parameters and definitions and step 2 defines the time domain weighting. Step 3 is the complex baseband transmitted signal z(i).OFDMA encoding for transmitter  (2)                1 Parameters and definitions from 1 in equation (1) and        
                              h          ⁡                      (            i            )                          =                ⁢                  20          ⁢                                          ⁢          Mhz          ⁢                                          ⁢          band          ⁢                                          ⁢          filter          ⁢                                          ⁢          impulse          ⁢                                          ⁢          response                                                  p          ⁡                      (            i            )                          =                ⁢                  impulse          ⁢                                                            ⁢                                                          ⁢          response          ⁢                                          ⁢          of          ⁢                                          ⁢          the          ⁢                                          ⁢          DFT          ⁢                                          ⁢          waveform                                        =                ⁢                  real          ⁢                                          ⁢          weighting          ⁢                                          ⁢          function          ⁢                                          ⁢          in          ⁢                                          ⁢          6          ⁢                                          ⁢          in          ⁢                                          ⁢                      FIG            .                                                  ⁢            1                                                  N        =                ⁢                  64          ⁢                                          ⁢          point          ⁢                                          ⁢          DFT                                                  1          /          T                =                ⁢                  20          ⁢                                          ⁢          MHz          ⁢                                          ⁢          sample          ⁢                                          ⁢          rate          ⁢                                          ⁢          for          ⁢                                                            ⁢                                                          ⁢          DFT                                        ≥                ⁢                  complex          ⁢                                          ⁢          Nyquist          ⁢                                          ⁢          rate                                        NT        =                ⁢                  3.2          ⁢                                          ⁢          μs          ⁢                                          ⁢          DFT          ⁢                                          ⁢          length                                                  1          /          NT                =                ⁢                  0.3125          ⁢                                          ⁢          MHz          ⁢                                          ⁢          DFT          ⁢                                          ⁢          output          ⁢                                          ⁢          rate                                        =                ⁢                  DFT          ⁢                                          ⁢          channel          ⁢                                          ⁢          separation                                        =                ⁢                  DFT          ⁢                                          ⁢          tone          ⁢                                          ⁢          spacings                                                        52 channels are used: 4 pilot, 48 data            12 guard band channels for rolloff of the h(k)                        2 Pulse p and band filter h weighting for DFT basis vectors        
                                          p            _                    =                    ⁢                      p            ⁢                                                  ⁢            ©            ⁢                                                  ⁢            h                          ,                  convolution          ⁢                                          ⁢          of          ⁢                                          ⁢          p          ⁢                                          ⁢          and          ⁢                                          ⁢          h                                        =                ⁢                  filter          ⁢                                                            ⁢                                                          ⁢          transfer          ⁢                                          ⁢          function          ⁢                                          ⁢          in          ⁢                                                            ⁢                                                          ⁢          time          ⁢                                          ⁢          domain                                                ⁢                  for          ⁢                                                            ⁢                                                          ⁢          the          ⁢                                          ⁢          combined          ⁢                                          ⁢          h          ⁢                                          ⁢          and          ⁢                                          ⁢          p          ⁢                                          ⁢          filters                                                ⁢                  [                                                    p                _                            ⁡                              (                0                )                                      ,                                          p                _                            ⁡                              (                1                )                                      ,            …            ⁢                                                  ,                          p              ⁡                              (                                  N                  -                  1                                )                                              ]                                    3 Transmitted OFDMA encoded baseband signal z(i) for one data block        
                              d          ⁡                      (            k            )                          =                ⁢                  data          ⁢                                          ⁢          modulation          ⁢                                          ⁢          for          ⁢                                          ⁢          user          ⁢                                          ⁢          k                                        =                ⁢                  encoded          ⁢                                                            ⁢                                                          ⁢          amplitude          ⁢                                          ⁢                      A            ⁡                          (              k              )                                ⁢                                          ⁢          and          ⁢                                          ⁢          phase          ⁢                                          ⁢                      φ            ⁡                          (              k              )                                                                        x          ⁡                      (            k            )                          =                ⁢                  transmitted          ⁢                                          ⁢          symbol          ⁢                                          ⁢          encoded          ⁢                                          ⁢          with          ⁢                                          ⁢                      d            ⁡                          (              k              )                                                              =                ⁢                              A            ⁡                          (              k              )                                ⁢                      exp            ⁡                          (                              j                ⁢                                                                  ⁢                                  φ                  ⁡                                      (                    k                    )                                                              )                                                                        z          ⁡                      (            i            )                          =                ⁢                              FFT                          -              1                                ⁡                      [                                                            p                  _                                ⁡                                  (                  i                  )                                            ⁢                              x                ⁡                                  (                  k                  )                                                      ]                                                  =                ⁢                              N                          -              1                                ⁢                      Σ            k                    ⁢                                    p              _                        ⁡                          (              i              )                                ⁢                      x            ⁡                          (              k              )                                ⁢                                    E              *                        ⁡                          (                              k                ,                i                            )                                          
OFDMA for IEEE 802.11g has the strict orthogonality of the DFT(FFT) replaced by cross-correlations between the 48 channel tones and other impacts due to the band channelization and pulse weighting p{circle around (c)}h plus the time errors Δt and frequency errors Δf from synchronization errors, multi-path, propagation, and terminal stresses. These impacts on orthogonality are low enough to allow OFDMA to support higher values for the symbol signal-to-noise ratio S/N in the detection band that are required for higher order symbol modulations. The highest order symbol modulation currently is 64 state quadrature amplitude modulation 64-QAM corresponding to 6 bits per symbol where 6=log2(64) and log2(o) is the logarithm to the base 2. With rate 3/4 convolutional coding the highest information rate is 4.5 bits/symbol=6×3/4. Required S/N at a BER=1.0e−6 is approximately S/N˜19 dB.
OFDMA for IEEE 802.11g provides 48 channels over a 20 MHz frequency band at a symbol rate equal to 0.25 MHz=1/4.0 μs from 6 in FIG. 1 and for a maximum information rate equal to 4.5 bits/symbol this equals a burst rate of 54 MBps=4.5×48×0.25. Some spread spectrum properties are realized by hopping the 20 MHz band, shuffling the channel assignments over the 48 available channels for a user assigned to several channels in order to spread his transmissions over the band, and for “flash” ODFMA by a random hopping of each user channel across the 48 available channels within the band.
OFDMA receiver decoding of the OFDMA waveform in FIG. 1 is defined in equations (3) for the receiver and derives estimates of the transmitted symbols by implementing matched filter detection in the receiver.OFDMA decoding for receiver  (3)
OFDMA decoding for one data block derives estimates
                    x        ^            ⁡              (        k        )              ⁢                  ⁢    of    ⁢                  ⁢          x      ⁡              (        k        )              ⁢                              ⁢                            ⁢    from    ⁢                  ⁢    the    ⁢                              ⁢                            ⁢    receiver    ⁢                              ⁢                            ⁢    estimates    ⁢                  ⁢                  z        ^            ⁡              (        i        )              ⁢                  ⁢    of    ⁢                  ⁢          z      ⁡              (        i        )                                                                    x              ^                        ⁡                          (              k              )                                =                    ⁢                      FFT            ⁡                          [                                                                    z                    ^                                    ⁡                                      (                    i                    )                                                  ⁢                ©                ⁢                                  p                  _                                            ]                                                                    =                    ⁢                                    Σ              i                        ⁢                                          z                ^                            ⁡                              (                i                )                                      ⁢            ©            ⁢                          p              _                        ⁢                          E              ⁡                              (                                  k                  ,                  i                                )                                                                                  ≅                    ⁢                      x            ⁡                          (              k              )                                          
Current CDMA spread spectrum art is illustrated by the waveform in FIG. 2 which describes the waveform for full band CDMA communications over the band B 9 which is the output range a of the band filter h(f) 7. The CDMA chip rate 1/Tc 12 is less than the available frequency band B to allow the chip frequency spectrum p(f) 10,11 to roll off. As defined 9 in FIG. 2 the band B and chip rate are related by equation B=(1+α)/Tc where α is the bandwidth expansion factor close to α=0.25 for high performance communications. Frequency spectrum p(f) 10 for the CDMA communications is essentially equal to the representative time pulse p(t) is a square-root raised cosine pulse which can be used for high performance communications to obtain a reasonably flat spectrum with a sharp rolloff at the edges to enable the chip rate 1/Tc to be reasonably close to the available frequency band B.
Chip rate 1/Tc is the CDMA total symbol rate. The users could be at different data rates but this and other architectural variations do not limit the scope of this invention. Power is uniformly spread over the CDMA pulse waveform spectrum p(f).
It is self evident to anyone skilled in the CDMA communications art that these communications mode assumptions are both reasonable and representative of the current CDMA art and do not limit the applicability of this invention.
CDMA encoding of the waveform in FIG. 2 for the transmitter is defined in equations (4). Steps 1,2 define the CDMA transmission and parameters. Step 3 defines the user symbol x(u). Step 4 is the set of Walsh orthogonal channelization codes w(u) and step 5 is the pseudo-random PN covering or spreading code. Step 6 defines the complex baseband signal z(t) as the waveform p(t−nTc) multiplied by the encoded sum over u and n.
where
                                          p            _                    ⁡                      (                          t              -                              nT                c                                      )                          =                ⁢                              p            ⁡                          (                              t                -                                  nT                  c                                            )                                ⁢                      ©h            ⁡                          (              t              )                                                              =                ⁢                  convolution          ⁢                                          ⁢          of          ⁢                                          ⁢                      p            ⁡                          (                              t                -                                  nT                  c                                            )                                ⁢                                          ⁢          and          ⁢                                          ⁢          h                                        =                ⁢                  filter          ⁢                                                            ⁢                                                          ⁢          transfer          ⁢                                          ⁢          function          ⁢                                          ⁢          in          ⁢                                                            ⁢                                                          ⁢          time          ⁢                                          ⁢          domain                                                ⁢                  for          ⁢                                                            ⁢                                                          ⁢          the          ⁢                                          ⁢          combined          ⁢                                                            ⁢                                                          ⁢                      p            ⁡                          (                              t                -                                  nT                  c                                            )                                ⁢                                          ⁢          and          ⁢                                          ⁢          h          ⁢                                          ⁢          filters                    
2 Parameters and definitions                Nc=Number of users and orthogonal code chips        Tc=CDMA chip length or repetition interval        1/NcTc=User symbol rate        
3 User complex signal x(i)
                              d          ⁡                      (            u            )                          =                ⁢                  data          ⁢                                          ⁢          modulation          ⁢                                          ⁢          for          ⁢                                                            ⁢                                                          ⁢          user          ⁢                                          ⁢          u                                                  =                    ⁢                      encoded            ⁢                                                  ⁢            amplitude            ⁢                                                  ⁢                          A              ⁡                              (                u                )                                      ⁢                                                  ⁢            and            ⁢                                                  ⁢            phase            ⁢                                                  ⁢                          φ              ⁡                              (                u                )                                                    ⁢                                                                    x          ⁡                      (            u            )                          =                ⁢                  transmitted          ⁢                                          ⁢          symbol          ⁢                                          ⁢          encoded          ⁢                                          ⁢          with          ⁢                                          ⁢                      d            ⁡                          (              u              )                                                              =                ⁢                              A            ⁡                          (              u              )                                ⁢                                          ⁢                      exp            ⁡                          (                              j                ⁢                                                                  ⁢                                  φ                  ⁡                                      (                    u                    )                                                              )                                          
4 Walsh orthogonal channelization code matrix W
                              W          =                    ⁢                      Code            ⁢                                                                      ⁢                                                                    ⁢            matrix                          ,                                  ⁢                              N            c                    ⁢                                                            ⁢                                                          ⁢          rows          ⁢                                          ⁢          of          ⁢                                          ⁢                      N            c                    ⁢                                          ⁢          code          ⁢                                          ⁢          vectors                                        =                ⁢                              [                          W              ⁡                              (                                  k                  ,                  n                                )                                      ]                    ⁢                                          ⁢          matrix          ⁢                                          ⁢          of          ⁢                                          ⁢          elements          ⁢                                          ⁢                      C            ⁡                          (                              k                ,                n                            )                                                                                    W            ⁡                          (                              u                ,                n                            )                                =                    ⁢                      +                          /                              -                1                                                    ,                  chip          ⁢                                          ⁢          n          ⁢                                          ⁢          of          ⁢                                          ⁢          vector          ⁢                                          ⁢          u                                                              W            ⁡                          (              u              )                                =                    ⁢                      code            ⁢                                                                      ⁢                                                                    ⁢            vector            ⁢                                                                      ⁢                                                                    ⁢            u                          ,                  row          ⁢                                          ⁢          k          ⁢                                          ⁢          of          ⁢                                          ⁢          W                                        =                ⁢                  [                                    W              ⁡                              (                                  u                  ,                  0                                )                                      ,                          W              ⁡                              (                                  u                  ,                  1                                )                                      ,            …            ⁢                                                  ,                          W              ⁡                              (                                  u                  ,                                                            N                      c                                        -                    1                                                  )                                              ]                    
5 PN covering (spreading) code P(n) for chip nP(n)=exp(jφ(n))
6 Transmitted CDMA complex baseband signal z(t)z(t)=Nc−1ΣuΣnP(n)W(u,n)×(u)p(t−nTc)
CDMA decoding of the waveform in FIG. 2 for the transmitter is defined in equations (5). Step 1 defines the convolution R(n,n−n′) of the CDMA pulse waveform with itself in the matched filter receiver. Steps 2,3 are the Walsh and PN decoding properties. Step 4 uses the matched filter detection theorem to derive the estimates of the transmitted symbols.CDMA decoding for receiver  (5)                1 Parameters and definitions are defined in 1,2,3 in equations (4) together withR(n,n−n′)=convolution of p(t−nTc) with        
                    p        _            ⁡              (                  t          -                                    n              ′                        ⁢                          T              c                                      )              ⁢                  ⁢    evaluated    ⁢                  ⁢    at    ⁢                  ⁢    the    ⁢                  ⁢    receiver              detection      ⁢                          ⁢      times      ⁢                          ⁢      t        =          nT      c                                    =                    ⁢                                    R              ⁡                              (                n                )                                      ⁢                          δ              ⁡                              (                                  n                  -                                      n                    ′                                                  )                                                                                  =                    ⁢                                                    R                ⁡                                  (                  n                  )                                            ⁢                                                          ⁢              for              ⁢                                                          ⁢              n                        =                          n              ′                                                                    =                    ⁢                      0            ⁢                                                  ⁢            otherwise                                              2 Walsh decoding of channelization codes W(k)WW*=NcI                     where I=Nc×Nc identify matrix                            W*=conjugate transpose of W<W(k),W(k′)>=Nδ(k−k′)                                                3 PN decodingP(n)P*(n)=1 for all n                     where P*=complex conjugate of P                        4 CDMA decoding{circumflex over (x)}(k)=ΣnP*(n)W*(k,n) {circumflex over (z)}(t){circle around (c)}p(t−nTc)        
It should be obvious to anyone skilled in the communications art that these example implementation algorithms in equations (1), (2), (3), (4), (5) clearly define the fundamental OFDMA and CDMA signal processing relevant to this invention disclosure and it is obvious that this example is representative of the other possible signal processing approaches.
For cellular applications the encoding algorithms for the transmitter describe the implementation of OFDMA and of CDMA encoding and are the transmission signal processing applicable to this invention for both the hub and user terminals, and the decoding algorithms for the receiver describes the corresponding OFDMA and CDMA receiving signal processing for the hub and user terminals for applicability to this invention.
For optical communications applications the microwave processing at the front end of both the transmitter and the receiver is replaced by the optical processing which performs the complex modulation for the optical laser transmission in the transmitter and which performs the optical laser receiving function of the microwave processing to recover the complex baseband received signal with the remainder of the signal processing functionally the same for the OFDMA and for the CDMA encoding transmitter and functionally the same as described for the OFDMA and CDMA receiving signal processing receiver.